Theorems · Theorem · linear algebra

linearIndependent_span

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M], LinearIndependent R v → LinearIndependent R fun i => ⟨v i, ⋯⟩

Defined in: Mathlib.LinearAlgebra.LinearIndependent.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Submodulestatement · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Submodule.spanstatement and proof · cited by 1,504
LinearIndependentstatement and proof · cited by 560
Submodule.subtypeproof · cited by 480
Set.mem_range_selfstatement · cited by 328
Submodule.subset_spanstatement · cited by 234
LinearIndependent.of_compproof · cited by 19

Cited by3

Results whose statement or proof uses this declaration.

Module.Basis.spanproof · cited by 11
Module.Basis.span_applyproof · cited by 8
Module.Basis.span_repr_eq_singleproof · cited by 1